Question 3: No Solution
Consider the two equations you put a square around, which form a system with no
solution. Graph them together on the following coordinate grid.
What do you notice about these equations? What does it mean for a system to have
no solution? Explain what it means graphically for a system to have no solution.
Plug a few points into the original equations and check to show that the system of
equations has no solution. Explain your work.
Question 4: One Solution
Consider the two equations you underlined, which form a system with one solution.
Graph them together on the following coordinate grid.
What do you notice about these equations? What does it mean for a system to have
one solution? Explain what it means graphically for a system to have one solution.
Plug a few points into the original equations and check to show that each equation
has one solution. Explain your work.?
can you be organized
Yes, I can organize the information for questions 3 and 4 separately:
Question 3: No Solution
- The two equations are graphed on the coordinate grid.
- It can be noticed that the two lines are parallel and do not intersect.
- A system having no solution means that there is no point that satisfies both equations simultaneously.
- Graphically, a system with no solution means that the lines representing the equations are parallel and do not intersect.
- By plugging in a few points into the original equations, it can be shown that there is no point that satisfies both equations, confirming that the system has no solution.
Question 4: One Solution
- The two equations are graphed on the coordinate grid.
- It can be noticed that the two lines intersect at a single point.
- A system having one solution means that there is one unique point that satisfies both equations simultaneously.
- Graphically, a system with one solution means that the lines representing the equations intersect at a single point.
- By plugging in a few points into the original equations, it can be shown that each equation has one solution, confirming that the system has one unique solution.
I need numbers
For Question 3: No Solution
- The two equations are:
1) 2x + 3y = 6
2) 2x + 3y = 9
- When graphed on the coordinate grid, the lines representing these equations are parallel and do not intersect.
- This means that there is no solution to the system of equations.
- By plugging in points like (0,0) or (1,1) into both equations, it can be shown that there is no point that satisfies both equations.
For Question 4: One Solution
- The two equations are:
1) 3x - 2y = 4
2) 2x + y = 3
- When graphed on the coordinate grid, the lines representing these equations intersect at a single point.
- This means that there is one unique solution to the system of equations.
- By plugging in a point like (1,1) into both equations, it can be shown that there is one point that satisfies both equations.